Accessible AC (#4)

Electricity and Magnetism Level 1

Let X C X_C be a positive real number representing the capacitive reactance (in ohms) associated with a capacitor at an angular frequency ω \omega .

Calculate the following for ( C = 1 20 F ) (C = \frac{1}{20} \text{F}) and ( ω = 10 rad/s ) (\omega = 10 \, \text{rad/s}) :

d X C d ω = ? \large{\frac{d X_C}{d \omega} = ?}


The answer is -0.2.

Steven Chase by Steven Chase , 37, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Steven Chase
Dec 16, 2017

The expression for capacitive reactance is:

X C = 1 ω C = ω − 1 1 C X_C = \frac{1}{\omega C} = \omega^{-1} \frac{1}{C}

Differentiating with respect to angular speed:

d X C d ω = − ω − 2 1 C = − 1 ω 2 C \frac{d X_C}{d \omega} = -\omega^{-2} \frac{1}{C} = -\frac{1}{\omega^2 C}

Plugging in numbers:

d X C d ω = − 1 1 0 2 / 20 = − 1 5 = − 0.2 \frac{d X_C}{d \omega} = -\frac{1}{10^2 / 20} = -\frac{1}{5} = -0.2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...